A classic problem from chemistry is used to test a conjecture that in domains for which data are most naturally represented by graphs, theories constructed with Inductive Logic Programming (ILP) will significantly outperform those using simpler feature-based methods. One area that has long been associated with graph-based or structural representation and reasoning is organic chemistry. In this field, we consider the problem of predicting the mutagenic activity of small molecules: a property that is related to carcinogenicity, and an important consideration in developing less hazardous drugs. By providing an ILP system with progressively more structural information concerning the molecules, we compare the predictive power of the logical theories constructed against benchmarks set by regression, neural, and tree-based methods. 1 Introduction Constructing theories to explain observations occupies much of the creative hours of scientists and engineers. Programs from the field of Inductiv...

Recently, computer programs developed within the field of Inductive Logic Programming have received some attention for their ability to construct restricted first-order logic solutions using problem-specific background knowledge. Prominent applications of such programs have been concerned with determining "structure-activity" relationships in the areas of molecular biology and chemistry. Typically the task here is to predict the "activity" of a compound, like toxicity, from its chemical structure.

Inductive Logic Programming (ILP) involves learning relational concepts from examples and background knowledge. To date all ILP learning systems make use of tests inherited from propositional and decision tree learning for evaluating the significance of hypotheses. None of these significance tests take account of the relevance or utility of the background knowledge. In this paper we describe a method, called HP-compression, of evaluating the significance of a hypothesis based on the degree to which it allows compression of the observed data with respect to the background knowledge. This can be measured by comparing the lengths of the input and output tapes of a reference Turing machine which will generate the examples from the hypothesis and a set of derivational proofs. The model extends an earlier approach of Muggleton by allowing for noise. The truth values of noisy instances are switched by making use of correction codes. The utility of compression as a significance measure is evaluated empirically in three independent domains. In particular, the results show that the existence of positive compression distinguishes a larger number of significant clauses than other significance tests The method is also shown to reliably distinguish artificially introduced noise as incompressible data.

All generalisations within logic involve inverting implication. Yet, ever since Plotkin's work in the early 1970's methods of generalising first-order clauses have involved inverting the clausal subsumption relationship. However, even Plotkin realised that this approach was incomplete. Since inversion of subsumption is central to many Inductive Logic Programming approaches, this form of incompleteness has been propagated to techniques such as Inverse Resolution and Relative Least General Generalisation. A more complete approach to inverting implication has been attempted with some success recently by Lapointe and Matwin. In the present paper the author derives general solutions to this problem from first principles. It is shown that clausal subsumption is only incomplete for self-recursive clauses. Avoiding this incompleteness involves algorithms which find "nth roots" of clauses. Completeness and correctness results are proved for a non-deterministic algorithms which constructs nth ro...

. This paper is concerned with problems that arise when submitting large quantities of data to analysis by an Inductive Logic Programming (ILP) system. Complexity arguments usually make it prohibitive to analyse such datasets in their entirety. We examine two schemes that allow an ILP system to construct theories by sampling from this large pool of data. The first, "subsampling", is a single-sample design in which the utility of a potential rule is evaluated on a randomly selected sub-sample of the data. The second, "logical windowing", is multiplesample design that tests and sequentially includes errors made by a partially correct theory. Both schemes are derived from techniques developed to enable propositional learning methods (like decision trees) to cope with large datasets. The ILP system CProgol, equipped with each of these methods, is used to construct theories for two datasets -- one artificial (a chess endgame) and the other naturally occurring (a language tagging problem). I...

Given sample data and background knowledge encoded in the form of logic programs, a predictive Inductive Logic Programming (ILP) system attempts to nd a set of rules (or clauses) for predicting classi- cation labels in the data. Most present-day systems for this purpose rely on some variant of a generate-and-test procedure that repeatedly examines a set of potential candidates (termed here as the \search space") and selects one or more clauses according to some criterion of \goodness". The worst-case time-complexity of such systems depends critically on: (1) the size of the search space; and (2) the cost of estimating the goodness of a clause. This paper is concerned with addressing the rst issue and is motivated by two principal factors. First, the representation adopted by an ILP system often engenders a search space whose size dominates complexity calculations. Straightforward arguments show that examining fewer clauses should lead to faster execution times. Second,...

Inductive Logic Programming (ILP) systems construct explanations for data in terms of domain-specific background information. How does the quality of this information affect the performance of an ILP system? Results from experiments concerned with learning simple programs for list processing suggest that performance is sensitive to the type and amount of background knowledge provided. In particular, background knowledge that contains large amounts of information that is known to be irrelevant to the problem being considered can, and typically does, prevent an ILP system in its search for an correct explanation.

Using problem-specific background knowledge, computer programs developed within the framework of Inductive Logic Programming (ILP) have been used to construct restricted first-order logic solutions to scientific problems. However, their approach to the analysis of data with substantial numerical content has been largely limited to constructing clauses that: (a) provide qualitative descriptions ("high", "low" etc.) of the values of response variables; and (b) contain simple inequalities restricting the ranges of predictor variables. This has precluded the application of such techniques to scientific and engineering problems requiring a more sophisticated approach. A number of specialised methods have been suggested to remedy this. In contrast, we have chosen to take advantage of the fact that the existing theoretical framework for ILP places very few restrictions of the nature of the background knowledge. We describe two issues of implementation that make it possible to us...

Given domain-specific background knowledge and data in the form of examples, an Inductive Logic Programming (ILP) system extracts models in the data-analytic sense. We view the model-selection step facing an ILP system as a decision problem, the solution of which requires knowledge of the context in which the model is to be deployed. In this paper, "context" will be defined by the current specification of the prior class distribution and the client's preferences concerning errors of classification. Within this restricted setting, we consider the use of an ILP system in situations where: (a) contexts can change regularly. This can arise for example, from changes to class distributions or misclassification costs; and (b) the data are from observational studies. That is, they may not have been collected with any particular context in mind. Some repercussions of these are: (a) any one model may not be the optimal choice for all contexts; and (b) not all the background information provided may be relevant for all contexts. Using results from the analysis of Receiver Operating Characteristic curves, we investigate a technique that can equip an ILP system to reject those models that cannot possibly be optimal in any context. We present empirical results from using the technique to analyse two datasets concerned with the toxicity of chemicals (in particular, their mutagenic and carcinogenic properties). Clients can and typically do, approach such datasets with quite different requirements. For example, a synthetic chemist would require models with a low rate of commission errors which could be used to direct efficiently the synthesis of new compounds. A toxicologist on the other hand, would prefer models with a low rate of omission errors. This would enable a more complete identificati...

Inductive Logic Programming (ILP) systems have had noteworthy successes in extracting comprehensible and accurate models for data drawn from a number of scientifc and engineering domains. These results suggest that ILP methods could enhance the model-construction capabilities of software tools being developed for the emerging discipline of "knowledge discovery from databases." One significant concern in the use of ILP for this purpose is that of efficiency. The performance of modern ILP systems is principally affected by two issues: (1) they often have to search through very large numbers of possible rules (usually in the form of definite clauses); (2) they have to score each rule on the data (usually in the form of ground facts) to estimate "goodness". Stochastic and greedy approaches have been proposed to alleviate the complexity arising from each of these issues. While these techniques can result in order-of-magnitude improvements in the worst-case search complexity of an ...